We in­vest­ig­ate the nature of the set of empti­ness times of a dam whose re­lease rate de­pends on the con­tent and whose cu­mu­lat­ive in­put pro­cess is a pure-jump Lévy pro­cess. De­tailed res­ults are ob­tained for stable in­put pro­cesses and re­lease func­tions of the form \( r(x) = x^{\beta}I_{(0,\infty)}(x) \)

Is math­em­at­ics use­ful? We who are en­gaged in the pro­fes­sion must have had oc­ca­sions to won­der about this ques­tion. It is of­ten said that math­em­at­ics is not really a sci­ence; it is an art. It is an art in the sense that in its pur­suit we strive for beauty, not util­ity. If we study math­em­at­ics as an art, per­haps we can jus­ti­fy it for its own sake, al­though there are some people who would dis­par­age “art for art’s sake”. When it comes to sci­ence, there is more reas­on to ask wheth­er it is use­ful. Does it ap­ply to the prac­tic­al needs of our daily life? Does it con­trib­ute to the gen­er­al well-be­ing of so­ci­ety and man­kind?

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